The purpose of this study is to determine how effective treatment with tirapazamine and cisplatin is in treating advanced cervical cancer. At present, cervical cancer is the fourth most common malignancy in American women, and the second leading cause of death from gynecologic malignancy. Therapeutic outcome for cervical carcinoma which is refractory or recurrent following primary therapy remains disappointing. Thus, research is ongoing to identify more effective chemotherapeutic regimens for this disease. This cancer is a relatively chemoresistant tumor, and the efficacy is often further diminished by complications of prior radiation therapy. Additionally, the contribution of bulky tumor masses and poor blood supply often results in a hypoxic environment for a large percentage of tumor cells which limits the efficacy of most standard chemotherapeutic agents. Tirapazamine is an investigational chemotherapeutic agent which was specifically developed to have increased activity against hypoxic cells. The present study has been designed to study the efficacy and toxicities associated with a combination of cisplatin plus tirapazamine administered every 21 days in patients with recurrent or refractory cervix cancer.